On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity

Marc Olive (1) , Boris Desmorat (2) , Boris Kolev (1) , Rodrigue Desmorat (1)

1 LMT - Laboratoire de mécanique et technologie
2 DALEMBERT - Institut Jean Le Rond d'Alembert

We formulate necessary and sufficient conditions for a unit vector n to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the components of n. Compared to Cowin-Mehrabadi conditions, this is an improvement, since these equations involve only the normal vector n to the plane symmetry (and no vector perpendicular to n). Similar reduced algebraic conditions are obtained for linear piezo-electricity and for totally symmetric tensors up to order 6.

Mots clés: Anisotropy; Elasticity; Material symmetry; Piezo-electricity

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Marc Olive, Boris Desmorat, Boris Kolev, Rodrigue Desmorat. On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity. Journal of Elasticity, 2020, 141 (1), pp.147-163. ⟨10.1007/s10659-020-09778-5⟩. ⟨hal-02516951v2⟩